Ice layer

A 2 cm thick layer of ice formed in the circular water tank. What part of the tank's water (answer in percent) froze if the tank has a diameter of 20 m and a depth of 1.5 m?

Final Answer:

p =  1.3333 %

Step-by-step explanation:

$$\begin{gathered} h_1=2\text{cm}\to \text{m}=2:100\text{m}=0.02\text{m} \\ D=20\text{m} \\ {h}_2=1.5\text{m} \\ r=D/2=20/2=10\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 10^2\doteq 314.1593{\text{m}}^2 \\ {V}_1=S\cdot h_1=314.1593\cdot 0.02\doteq 6.2832{\text{m}}^3 \\ {V}_2=S\cdot h_2=314.1593\cdot 1.5\doteq 471.2389{\text{m}}^3 \\ p=100\cdot \frac{V_1}{V_2}=100\cdot \frac{6.2832}{471.2389}=\frac{4}{3}\doteq 1.3333\% \\ {p}_2=100\cdot \frac{h_1}{h_2}=100\cdot \frac{0.02}{1.5}=\frac{4}{3}\doteq 1.3333\% \\ p=p_2=1.3333=1.3333\% \end{gathered}$$

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